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I have a kalman filter like set up, when I get the current value of an observable process, and update my estimate of the state variable with it.

However, my observations are non-uniform in time, and I am trying to add the logic, that if the last observation was really long ago, I should forget about it, and use an a priori estimate X.

I can just switch to X, if time since the last observation is > T. But I was hoping to put in some general setting, which will be consistent with the Kalman filter logic. Does anyone have suggestions/references for it?

Many thanks.

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  • $\begingroup$ If you are observing $V_t, V_{t-1}, \ldots$ to update the system state $X_t$, why not observe $(V_t, V_{t-1})$ jointly and update the state only when $V_t = V_{t-1}$? $\endgroup$ – AdamO Apr 13 '16 at 18:26
  • $\begingroup$ Sorry, I don't understand your suggestion. Say, I have a stream of observations: 3 at t_1, 5 at t_2, 3 at t_3, 5 at t_4 - are you suggesting to ignore all of those? $\endgroup$ – LazyCat Apr 13 '16 at 18:34
  • $\begingroup$ And are you directly observing a state here? For instance, you observe 3 at time 1, but does that mean the state is 3 at time 1... the observations need not be the states, you could be observing acceleration in a vehicle and predicting its location on a road for instance. $\endgroup$ – AdamO Apr 13 '16 at 18:46
  • $\begingroup$ Yes, for simplicity, assume, that we are observing the state. $\endgroup$ – LazyCat Apr 13 '16 at 18:50
  • $\begingroup$ Then my example would not yield any valid state for the observations you present. $\endgroup$ – AdamO Apr 13 '16 at 18:51
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If the Kalman filter-like model includes a covariance for the error-states, and if this covariance is being propagated in time such that it grows in the absence of new measurements, then a natural solution to the problem is to periodically check the trace of the error covariance against a ceiling threshold. If the threshold is exceeded we assume the filter has lost all useful information about the state, and that the state estimate should be reset to the a-priori value. Since the KF is usually a linearized approximation for a non-linear problem there is good reason to question the usefulness of the information stored in the covariance if the state error covariance is large.

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